Practices Worthy of Attention
Algebra for All
Norfolk Public Schools
Norfolk, Virginia
Summary of the Practice. Norfolk Public Schools has been working since 2000–2001 to
increase the number of students taking Algebra I in middle school with their Algebra for All
project. They have provided paid training for middle school teachers to become highly qualified
algebra instructors and have provided continual professional development and learning
communities for teachers to improve their content knowledge and instruction. Norfolk has also
provided resources to students during and after school, as well as in the summer, to hone their
mathematics skills, and they have created an aligned strand of algebraic concepts starting in
kindergarten.
Need. Algebra I often serves as a gatekeeper, helping determine whether students will be able to
access high levels of mathematics. Norfolk Public Schools wanted to find a way to close the
achievement gap and provide higher-quality mathematics learning starting at earlier grade levels.
Goal. Norfolk’s goal is to have all students master Algebra I before entering high school. They
hope to achieve this goal by 2012 (with measurable yearly targets).
Demographics
Norfolk Public Schools serves grades K–12. Enrollment was over 36,000 students in 2005–
2006, having decreased by about 700 students over the previous four years (see Table 1).
Table 1. Norfolk School District Enrollment Data
Academic Year
Enrollment
2002–2003
36,745
2003–2004
36,684
2004–2005
36,250
2005–2006
36,054
Table 2 shows the number and percentage of students enrolled and dropping out by
race/ethnicity and limited proficiency in English. As of 2005–2006, most students (69.7%) in
Norfolk were black, 24.6% of students were white, 3.3% Hispanic, and 2.2% Asian
American. About 1% of Norfolk students were classified as having limited English
proficiency. Dropout rates over the last few years have been low, about 1% to 2%.
Charles A. Dana Center at the University of Texas at Austin
1
Practices Worthy of Attention
Norfolk Public Schools
Table 2. Norfolk School District Enrollment and Dropout Rates
Demographics
All Students
Asian American
Black
Hispanic
White
Limited English
Proficient
Academic
Year
Number
Enrolled
Percentage
Enrolled
Percentage
Dropping Out
2002–2003
36,745
100
1.9
2003–2004
36,684
100
1.0
2004–2005
36,250
100
1.0
2005–2006
36,054
100
*
2002–2003
782
2.1
*
2003–2004
742
2.0
*
2004–2005
740
2.0
*
2005–2006
780
2.2
*
2002–2003
24,929
67.8
*
2003–2004
25,163
68.6
*
2004–2005
25,153
69.4
*
2005–2006
25,144
69.7
*
2002–2003
950
2.6
*
2003–2004
1,033
2.8
*
2004–2005
1,114
3.1
*
2005–2006
1,201
3.3
*
2002–2003
10,008
27.2
*
2003–2004
9,678
26.4
*
2004–2005
9,182
25.3
*
2005–2006
8,862
24.6
*
2002–2003
199
0.5
*
2003–2004
263
0.7
*
2004–2005
334
0.9
*
2005–2006
454
1.3
Note: The asterisk (*) notes that data were not available.
*
Description of the Practice
For years, algebra has been known as the gatekeeper to advanced mathematics in the high
schools of Norfolk Public Schools. A Norfolk district mathematics specialist said, “To realize
the district vision of equity and excellence, we must change the algebra course from a filter
that screens out segments of our population to a pump that propels all students toward
opportunity” (Norfolk Public Schools, 2006). In 2000–2001, Norfolk decided to set a goal of
having all students complete Algebra I in eighth grade.
Their reasoning was that, according to education research, the majority of college-bound
students take at least Algebra I and Geometry before graduating high school. For example, the
Charles A. Dana Center at the University of Texas at Austin
2
Practices Worthy of Attention
Norfolk Public Schools
National Educational Longitudinal Study (NELS) indicates that students who take rigorous
high school mathematics courses are much more likely to go to college than those who do not
(U.S. Department of Education, 1997). In fact, their data show that 83 percent of students
taking Algebra I and Geometry went to college within two years of graduating from high
school. This percentage drops to 36 percent for those who did not take Algebra I and
Geometry. Research suggests that specific courses, such as Algebra I, serve as gatekeepers to
high-level mathematics knowledge and can affect mathematics achievement in high school
and beyond (Adelman, 2006; Ma, 2001). Norfolk wanted to ensure that their students had
every opportunity to access not only Geometry in high school, but also Algebra II and other
higher-level mathematics; thus, they felt that getting students through Algebra I earlier would
create greater chances for students to take and excel in the higher-level courses.
With the Algebra for All project, as it was named, came a change in the thinking and
infrastructure in the mathematics department, as Norfolk realized that the project could not
just be about changing enrollment patterns, but rather must involve a true improvement in the
quality of mathematics instruction. Norfolk is fortunate in that Virginia has a statewide endof-course Algebra I exam, so they have been able to use results on the exam to measure how
well their students are doing as more eight-graders continue to enroll in Algebra I.
Norfolk has been addressing several issues as they have implemented their Algebra for All
project: equity and learning, curriculum, and instruction. In terms of equity and learning, the
district believes in setting high expectations and providing worthwhile learning opportunities
for all students. They work to accommodate differences to help all students learn mathematics
with resources and support for all classrooms and all students to help them succeed.
“Academic success sessions” provide student support during and after the school day, using
outside resources and technology like Apex Learning Math ClassTools and ExploreLearning
to help illustrate mathematical concepts.
The district also realizes that implementing the project requires several steps that depend on
having the right infrastructures in place. They set targets for Algebra I enrollment at each
middle school instead of setting a districtwide aggregate, hoping to accommodate schools at
their different levels and help them successfully reach their individual targets. Additionally,
counselors and mathematics teachers discuss the mathematics curriculum with parents and the
public to help them understand the changes in the curriculum and to explain the importance of
mathematics for students’ overall academic achievement.
In their curriculum, Norfolk focuses on vertical articulation and coherence of mathematics
across grades. The district realized that there needed to be a basis for algebra content in all
grades preceding the course, beginning in prekindergarten, as the National Academy Press
(1998) advises. Mathematics content staff integrated algebraic reasoning across all topics in
the grades K–7 curriculum in a coherent content strand involving patterns, functions, and
algebra. They said that their intention was to “algebra-fy” school mathematics.
The new articulation ensures a progression of concepts, so that when students reach Algebra I,
they will be prepared with basic algebraic ideas and concepts. In prekindergarten through
grade 4, for example, the focus of mathematics teaching is on developing a strong foundation
of numeracy, so that students are fluent with numbers as a tool for developing algebraic
Charles A. Dana Center at the University of Texas at Austin
3
Practices Worthy of Attention
Norfolk Public Schools
thinking. In middle school, the curriculum has been compacted and focuses on the concepts of
balance, proportional reasoning, multiplicative thinking, and the concept of a variable (which
is now introduced in grade 5). In grades 6 and 7, there is a double block of mathematics (90
minutes) every day to prepare students for Algebra I in eighth grade. Norfolk also developed
common districtwide Algebra I assessments for both middle school and high school,
administered in January and May, as item-level analyses of how middle and high school
students perform differently or similarly on Algebra I items.
Norfolk believes that qualified teachers (that is, those fully certified and with a full
endorsement in mathematics or an algebra add-on endorsement) are essential to higher student
achievement in mathematics. The district is requiring that teachers have thorough knowledge
and understanding of the mathematics they teach and is working on increasing the number of
middle school teachers with algebra add-on endorsements. From 2002–2003 to 2004–2005,
the percentage of middle school mathematics teachers with algebra add-on endorsements
increased from 32% to 40%. In 2005–2006, the percentage of middle school teachers with
algebra add-on endorsements varied across schools, from 33% up to 100%. Norfolk is also
providing incentives for teachers to fulfill the requirements of add-on endorsements by
providing tuition support. In addition, the district provides financial support to all middle
school mathematics teachers taking their PRAXIS (teacher certification) exams.
Norfolk provides professional development so that teachers have the training and support they
need to deliver high-quality mathematics instruction and ensure that all students are learning.
Teacher professional development is guided by three main ideas, as stated in Norfolk’s (n.d.)
Handbook for Teaching: (1) learning mathematics with conceptual understanding is essential,
(2) conceptual understanding is an important part of mathematics proficiency, and (3) learning
mathematics requires students to actively engage in tasks and experiences designed to deepen
and connect their knowledge of mathematics. In making connections explicit, some
professional development sessions focus on how children learn mathematics, as suggested by
the National Research Council (2001), teaching teachers about using concrete materials and
maximizing the application of concrete ideas into abstract ones.
K–8 teachers went through the Building a Foundation for Algebra professional development
session offered by Math Solutions. The purpose of this training was to help the teachers better
understand critical algebraic concepts through hands-on investigations and learn how to teach
concepts and skills that include patterns, equivalence, variables, multiple representations,
equations, graphing, and functions. All teachers in grades 7 and 8 were also trained in
implementing SpringBoard, a College Board program that helps teachers improve their
practice through four main steps: planning instruction that will develop students’ analytical,
problem-solving, and critical thinking skills; enhancing and complementing existing
curriculum and state standards; assessing student performance and learning whether students
can apply what they have learned in one context to a different one; and generating reports that
provide feedback about student learning and progress. Additional professional development
sessions include training on implementation of graphing calculators and use of Algeblocks.
Norfolk is also working on ways to develop an Algebra I study group within the district. For
instance, the district has found funding for release time so that Algebra I study groups for
middle school teachers can operate both during the school day and after school. The focus of
Charles A. Dana Center at the University of Texas at Austin
4
Practices Worthy of Attention
Norfolk Public Schools
these study groups is on examining student work and structuring lessons to incorporate
technology and concrete tools. Norfolk is also working to implement Blackboard, a webbased discussion board that can help keep teachers focused on issues in algebra between study
group sessions. Blackboard is used as a forum for teachers to ask questions, share ideas, and
recommend good instructional strategies on different topics.
Results
Table 3 lists the results for the past few years for Norfolk Public Schools on the Virginia
Standards of Learning test in mathematics. There are no clear patterns of improvement across
subgroups. In general, black students and students with economic disadvantage were the
lowest-performing students. Scores for students with limited proficiency in English have
decreased substantially over the past three years in eighth grade but have increased in high
school.
Table 3. Norfolk Public Schools Virginia Standards of Learning Mathematics Exam Results
Demographics
All Students
Asian American
Black
Hispanic
White
Limited English
Proficient
Economically
Disadvantaged
Academic
Year
Percentage Met/Exceeded Standard
Grade 8
High School
2003–2004
2004–2005
73
76
80
81
2005–2006
71
79
2003–2004
90
92
2004–2005
98
93
2005–2006
92
86
2003–2004
67
75
2004–2005
70
74
2005–2006
66
74
2003–2004
76
77
2004–2005
85
79
2005–2006
63
80
2003–2004
87
89
2004–2005
85
91
2005–2006
82
88
2003–2004
2004–2005
73
64
83
84
2005–2006
61
91
2003–2004
70
79
2004–2005
71
63
2005–2006
66
76
Charles A. Dana Center at the University of Texas at Austin
5
Practices Worthy of Attention
Norfolk Public Schools
As seen in Table 4, since 2002, the number of students passing Algebra I and the Algebra I
end-of-course exam in eighth grade has more than doubled.
Table 4. Number of Middle School Students in Norfolk Public Schools
Passing Algebra I Course and End-of-Course Exam
Academic Year
Number Passing Algebra I
Course and Test
2001–2002
364
2002–2003
424
2003–2004
552
2004–2005
778
2005–2006
869
Table 5 shows the number of Norfolk students enrolled in middle school Algebra I and the
number and percentage of those students who are black or white. In 2000–01, the year the
Algebra for All phase-in was launched, there was a higher percentage of white than black
students enrolled in eighth-grade Algebra I. The number and percentage of students enrolled
in Algebra I in middle school is gradually increasing, but the rate at which black student
enrollment is growing is still slower than the enrollment growth rate for white students. The
data in this table seem to suggest that Algebra for All is beginning to succeed in its enrollment
goals but is not yet moving Norfolk closer to its goal of providing more equitable preparation
for—and access to—Algebra I for all students in eighth grade. This slow growth rate may in
part be due to the gradual phase-in of the Algebra for All project.
Table 5. Algebra I Enrollment in Middle School (7th and 8th Grade) by Ethnicity
Academic
Year
Total
Number of
Students
Number of
Students in
Algebra I
Percentage of
Students in
Algebra I
Number and
Percentage of
Black Students
in Algebra I
Number and
Percentage of
White Students
in Algebra I
2000–2001
5,103
934
18%
416 (13%)
304 (21%)
2001–2002
5,336
875
16%
468 (14%)
382 (25%)
2002–2003
5,508
813
15%
460 (15%)
359 (25%)
2003–2004
5,566
1097
20%
449 (12%)
275 (19%)
2004–2005
5,435
1070
20%
582 (15%)
388 (27%)
2005–2006
5,283
1257
24%
572 (15%)
371 (29%)
The Getting Ready for Algebra (GRA) program has been in place in Norfolk since the
summer of 1996. This three-week, noncredit summer program targets rising eighth- and ninthgrade students enrolling in Algebra the next academic year. The program focuses on algebraic
topics such as proportional reasoning, the concept of variables, and the concept of balance.
Since Norfolk began focusing on Algebra I in 2000–2001, the number of students enrolled in
the GRA program has doubled, maintaining a high percentage passing the Algebra I end-ofcourse exam each year (see Table 6).
Charles A. Dana Center at the University of Texas at Austin
6
Practices Worthy of Attention
Norfolk Public Schools
Table 6. Getting Ready for Algebra (GRA) Passing Rates
Academic Year
Number of
Students Enrolled
Percentage of Students
Passing the Algebra I
End-of-Course Exam
2000–2001
57
96
2001–2002
71
96
2002–2003
107
95
2003–2004
92
97
2004–2005
94
*
Note: The asterisk (*) notes that data were not available.
Conclusions
Norfolk Public Schools won the 2005 Broad Prize for Urban Education, mainly due to its
data-driven system for monitoring student learning. Given Norfolk’s history as a U.S. Navy
transfer spot, having a high mobility rate of students (about 40%) is considered the norm, so
the district has worked for years to ensure they know where and when their students are
coming and going. Algebra for All has focused on several issues to improve the quality of
mathematics learning for all students. In the program’s five years, Norfolk has seen growth in
the number of students enrolling in and passing Algebra I in eighth grade. Norfolk’s goal is to
have all students passing Algebra I in eighth grade by 2012. They have been conscientious
about students’ and teachers’ morale in shifting to higher standards, and they work to provide
ways to have qualified, trained professionals help students pass Algebra I early so they can
gain access to higher-level mathematics in high school and college.
References
Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school
through college. Washington, DC: U.S. Department of Education.
Ma, X. (2001). A longitudinal assessment of antecedent course work in mathematics and
subsequent mathematical attainment. Journal of Educational Research, 94, 16-28.
National Academy Press. (1998). The nature and role of Algebra in the K-12 curriculum.
Washington, DC: Author.
National Research Council. (2001). Adding it up: Helping children learn mathematics.
Washington, DC: Author.
Norfolk Public Schools (2006). Algebra I report. Norfolk, VA: Author.
Norfolk Public Schools (n.d.). Handbook for teaching. Norfolk, VA: Author.
U.S. Department of Education. (1997). Mathematics equals opportunity. Washington, DC:
Author. Retrieved March 24, 2007, from http://www.ed.gov/pubs/math.
Charles A. Dana Center at the University of Texas at Austin
7
Practices Worthy of Attention
Norfolk Public Schools
About Practices Worthy of Attention: Local Innovations in Strengthening Secondary Mathematics
Practices Worthy of Attention is a joint initiative of Achieve, Inc. (www.achieve.org), and the Charles
A. Dana Center at The University of Texas at Austin (www.utdanacenter.org). The initiative is led by
Pamela L. Paek, a research associate at the Dana Center, who, in 2006, examined 22 program, school,
and district practices that showed promise—based on early evidence and observation—of strengthening
secondary mathematics teaching and learning.
Our goal was to document practitioners’ descriptions of what is really happening in the field to
strengthen secondary mathematics education around the country. Thus, while the practice highlighted
may be common, the specific structures and strategies used to implement the practice are worthy of
attention. These initial investigations set out to mark these practices for future rigorous scientific inquiry
by Dana Center and other researchers.
Ultimately, we hope to create a community of inquiry made up of university researchers working with
administrators and teachers from featured schools and districts to more rigorously research how
effectively these practices improve secondary mathematics learning for all students.
Reports and practice profiles. An executive summary details the methods for this initiative and
analyzes themes. Two cross-case analyses discuss specific strategies for raising student achievement
and building teacher capacity. Brief profiles describe each practice. All of these publications are
available on our website at www.utdanacenter.org.
Data. In all cases, data about the practice were provided by the program, school, or district studied as
part of a description of their practice. We did not independently analyze data gathered through a
consistent assessment tool, and we did not evaluate their uses of data for measuring effectiveness. Thus,
the data in the practice profiles are intended not to prove the practice’s effectiveness from a research
perspective, but to paint a detailed picture of the practice and what data were used by the program,
school, or district to gauge how well it was working.
Theoretical frameworks. In some cases, district staff mentioned specific literature on theory or
practice that they used when they developed the practice we highlight. In those cases, we cite that
literature in our discussion of the practice.
How to cite this profile
Paek, P. L. (2008, January). Algebra for All: Norfolk Public Schools. Case study from Practices worthy of
attention: Local innovations in strengthening secondary mathematics. Austin, TX: Charles A. Dana Center at
The University of Texas at Austin.
Charles A. Dana Center at the University of Texas at Austin
8